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Score : $300$ points

### Problem Statement

You are given an integer sequence of length $N$. The $i$-th term in the sequence is $a_i$. In one operation, you can select a term and either increment or decrement it by one.

At least how many operations are necessary to satisfy the following conditions?

• For every $i$ $(1≤i≤n)$, the sum of the terms from the $1$-st through $i$-th term is not zero.
• For every $i$ $(1≤i≤n-1)$, the sign of the sum of the terms from the $1$-st through $i$-th term, is different from the sign of the sum of the terms from the $1$-st through $(i+1)$-th term.

### Constraints

• $2 ≤ n ≤ 10^5$
• $|a_i| ≤ 10^9$
• Each $a_i$ is an integer.

### Input

Input is given from Standard Input in the following format:

$n$
$a_1$ $a_2$ $...$ $a_n$


### Output

Print the minimum necessary count of operations.

### Sample Input 1

4
1 -3 1 0


### Sample Output 1

4


For example, the given sequence can be transformed into $1, -2, 2, -2$ by four operations. The sums of the first one, two, three and four terms are $1, -1, 1$ and $-1$, respectively, which satisfy the conditions.

### Sample Input 2

5
3 -6 4 -5 7


### Sample Output 2

0


The given sequence already satisfies the conditions.

### Sample Input 3

6
-1 4 3 2 -5 4


### Sample Output 3

8